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Compact H$^-$ cyclotrons are used all across the globe to produce medical isotopes. Machines with external ion sources have demonstrated average extracted currents on the order of a few mA, although reported operational numbers are typically around 1\,mA or below. To explore the possibility of extracting even more current from such cyclotrons, it is important to understand the mechanisms that drive intensity limits and how they scale. In this paper we review some of the key aspects of the beam dynamics in the central region of compact cyclotrons, including rf electric focusing and space charge effects. We derive the scaling of the phase acceptance with the rf gap voltage, harmonic number, etc. We also explore the scaling with different types of ions such as H$^-$, H$_2^+$ and H$_3^+$. We discuss the impact of mechanical erosion of the central region electrodes. Thoughout the paper, we use examples and experimental data from two compact H$^-$ cyclotrons for reference: the TR-30 series and the TRIUMF 500\,MeV machine.

An accurate and detailed field map is important for cyclotron beam dynamics studies. During the long history of cyclotron studies, many techniques have been developed by cyclotron pioneers for the treatment of median plane field map. In this paper, we take the TRIUMF 500 MeV cyclotron as an example to study the asymmetric field resulting from the imperfect median plane symmetry. The ``Gordon approach'' and a highly accurate compact finite differentiation method are used to investigate the historical field survey data. The redundancy in the survey data is revealed by the expansion method, which also makes it possible to correct the error in the measurement. Finally, both the azimuthal field $B_\theta$ and the axial gradient of the axial field $dB_z/dz$ in the median plane are corrected using the radial field map $B_r$. The influence of the correction is examined by recalculating the equilibrium orbit properties of the TRIUMF cyclotron. The result shows significantly increased vertical centering errors of the closed orbits. Further simulation study suggests that these centering errors can be reduced to below 1.5 cm by adjusting the trim coils' $B_r$ field within the output limits of our trim coils' power supplies. The error in the measurement field data may explain why the calculated trim coils' settings during the cyclotron commissioning in 1974 encountered difficulty.

The precise diagnosis is of great significance in developing precise treatment plans to restore neck function and reduce the burden posed by the cervical spondylosis (CS). However, the current available neck function assessment method are subjective and coarse-grained. In this paper, based on the relationship among CS, cervical structure, cervical vertebra function, and surface electromyography (sEMG), we seek to develop a clustering algorithms on the sEMG data set collected from the clinical environment and implement the division. We proposed and developed the framework EasiCS, which consists of dimension reduction, clustering algorithm EasiSOM, spectral clustering algorithm EasiSC. The EasiCS outperform the commonly used seven algorithms overall.

Under research for near sixty years, Bose-$\!$Ray-$\!$Chaudhuri-$\!$Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions of some BCH codes of length $n=2^m+1$ with $m=2t+1$, $4t+2$, $8t+4$ and $m\geq 10$. Some new techniques are employed to investigate coset leaders modulo $n$. For each type of $m$ above, the first five largest coset leaders modulo $n$ are determined, the dimension of some BCH codes of length $n$ with designed distance $\delta>2^{\lceil \frac{m}{2} \rceil}$ is presented. These new techniques and results may be helpful to study other families of cyclic codes over finite fields.

Cavity optomechanics explores the coupling between the optical field and the mechanical oscillation to induce cooling and regenerative oscillation in a mechanical oscillator. So far, optomechanics relies on the detuning between the cavity and an external pump laser, where the laser acts only as a power supply. Here, we report a new scheme with mutual coupling between a mechanical oscillator that supports a mirror of a vertical-cavity surface-emitting laser (VCSEL) and the optical field, greatly enhancing the light-matter energy transfer. In this work, we used an ultra-light-weight (130 pg) high-contrast-grating (HCG) mirror in a VCSEL, whose reflectivity spectrum is designed to facilitate strong optomechanical coupling, to demonstrate optomechanically-induced regenerative oscillation of the laser optomechanical cavity with > 550 nm self-oscillation amplitude of the micro-mechanical oscillator, two to three orders of magnitude larger than typical. This new scheme not only offers an efficient approach for high-speed wavelength-swept sources, but also has far-reaching significance in the realization of quantum entanglement of macroscopic objects and ultrasensitive measurement of displacements and forces., Comment: 12 pages, 5 figures